R: Simulate Seasonal Persistent Processes Using the DWPT
dwpt.sim
R Documentation
Simulate Seasonal Persistent Processes Using the DWPT
Description
A seasonal persistent process may be characterized by a spectral
density function with an asymptote occuring at a particular frequency
in [0,1/2). It's time domain representation
was first noted in passing by Hosking (1981). Although an exact
time-domain approach to simulation is possible, this function utilizes
the discrete wavelet packet transform (DWPT).
Long-memory parameter for the seasonal persistent process.
fG
Gegenbauer frequency.
M
Actual length of simulated time series.
adaptive
Logical; if TRUE the orthonormal basis used in
the DWPT is adapted to the ideal spectrum, otherwise the orthonormal
basis is performed to a maximum depth.
epsilon
Threshold for adaptive basis selection.
Details
Two subroutines are used, the first selects an adaptive orthonormal
basis for the true spectral density function (SDF) while the second
computes the bandpass variances associated with the chosen orthonormal
basis and SDF. Finally, when code{M} > code{N} a
uniform random variable is generated in order to select a random piece
of the simulated time series. For more details see Whitcher (2001).
Value
Time series of length N.
Author(s)
B. Whitcher
References
Hosking, J. R. M. (1981)
Fractional Differencing,
Biometrika, 68, No. 1, 165-176.
Whitcher, B. (2001)
Simulating Gaussian Stationary Time Series with Unbounded Spectra,
Journal of Computational and Graphical Statistics, 10,
No. 1, 112-134.
See Also
hosking.sim for an exact time-domain method and
wave.filter for a list of available wavelet filters.
Examples
## Generate monthly time series with annual oscillation
## library(ts) is required in order to access acf()
x <- dwpt.sim(256, "mb16", .4, 1/12, M=4, epsilon=.001)
par(mfrow=c(2,1))
plot(x, type="l", xlab="Time")
acf(x, lag.max=128, ylim=c(-.6,1))
data(acvs.andel8)
lines(acvs.andel8$lag[1:128], acvs.andel8$acf[1:128], col=2)